Abstract
The question whether the preemptive Sum Multicoloring (pSMC) problem is hard on paths was raised by Halldórsson et al. in [8]. The pSMC problem is a scheduling problem where the pairwise conflicting jobs are represented by a conflict graph, and the time lengths of jobs by integer weights on the nodes. The goal is to schedule the jobs so that the sum of their finishing times is minimized. In the paper we give an \(\mathcal{O}(n^3p)\) time algorithm for the pSMC problem on paths, where n is the number of nodes and p is the largest time length. The result easily carries over to cycles.
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© 2004 Springer-Verlag Berlin Heidelberg
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Kovács, A. (2004). Sum-Multicoloring on Paths. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_7
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DOI: https://doi.org/10.1007/978-3-540-24749-4_7
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